Product Description

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite. Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enjoyable muscle flexing by a reader. The material is aimed at students and researchers in probability, statistics, financial engineering, mathematics, operations research, civil engineering and economics who need to know about: asymptotic methods for extremes; models for records and record frequencies; stochastic process and point process methods and their applications to obtaining distributional approximations; pervasive applications of the theory of regular variation in probability theory, statistics and financial engineering.

“This book is written in a very lucid way. The style is sober, the mathematics tone is pleasantly conversational, convincing and enthusiastic. A beautiful book!”

Bulletin of the Dutch Mathematical Society

“This monograph is written in a very attractive style. It contains a lot of complementary exercises and practically all important bibliographical reference.”

Revue Roumaine de Mathématiques Pures et Appliquées

Product Details

• Amazon Sales Rank: #856976 in Books
• Published on: 2007-11-26
• Original language: English
• Number of items: 1
• Binding: Paperback
• 320 pages

Review

"This book is written in a very lucid way. The style is sober, the mathematics tone is pleasantly conversational, convincing and enthusiastic. A beautiful book!"

---Bulletin of the Dutch Mathematical Society

"This monograph is written in a very attractive style. It contains a lot of complementary exercises and practically all important bibliographical reference."

---Revue Roumaine de Mathématiques Pures et Appliquées

Customer Reviews

excellent treatment of extremes including regular variation concept
When I was a graduate student at Stanford in the late 1970s Sid Resnick was an assistant professor there. I took a course in stochastic processes from him. His presentation was engaging and humorous as is his writing style. This is more readily appreciated in one of his other books "A Probability Path".
This is one of several good texts on the theory of extremes that came out in the 1980s. The book is rigorous and formal and deals primarily with the iid case (the exception is extremes of moving averages). It differs from the others in that it treats the relationship between extremes and record values.

Resnick also deals with a characterization of tail behavior called regular variation that is a very useful tool in developing some of the theory. Like Leadbetter et al. he uses the point process approach but he does not exploit its application to stationary processes the way they do.

In the 1980s Resnick went on to Colorado State University where he had a very fruitful collaboration with Richard Davis. That is where he was at teh time of this text and the results of their joint research is reflected in the text. It also includes material on multivariate extremes and extremal processes.

Currently Resnick is a professor of statistics and operations research at Cornell University. This was one of Resnick's early works and is now available in a less expensive paperback editon.

extreme values at their extremities
superbly written, lucid , clear text communicating fundamental concepts of basic stochastic processes, probability theory in a fashion, books designed for those subjects fall woefully short relative to resnick's exposition. extreme value theory is clearly presented in a fashion which makes it look easy!